How to build a rectangle with convex edges and rounded corners?
I suggest you this: if the exact shape is important, trace the bitmap to svg, then import the svg and import it to Blender, convert to mesh, clean the mesh... done! Here it goes:

Open Inkscape, paste the png and trace it like this:



you need to clean the traced paths, delete whatever is not your desired shapes...

then delete the bitmap, save the svg and import it in Blender: scale the imported curve enough (I did 50x), and put "geometry to the center" using the toolbox function (left panel).



then, convert curve to mesh, and change material color if you wish:





Then, convert all mesh triangles (many) to simple ngons, using limited dissolve:



there you are! Of course you have many vertices...



Of course you could also just keep the vector/curves....